Maximizing Revenue from Ticket Sales

The video tutorial explains how to maximize revenue for a baseball stadium by adjusting ticket prices. It assumes a linear relationship between ticket price and attendance, using given data points to derive a linear equation for attendance. The revenue function is formulated as a product of price and attendance, and calculus is used to find the price that maximizes revenue. The critical point is verified using the second derivative test, confirming that a ticket price of $10.10 maximizes revenue.

What is the initial average attendance when the ticket price is $11?

• 56,000

• 28,000

• 23,000

• 50,500

What happens to the average attendance when the ticket price is reduced to $9?

• It remains the same

• It decreases to 23,000

• It increases to 28,000

• It decreases to 20,000

What is the slope of the linear relationship between ticket price and attendance?

• -2500

• 2500

• -5000

• 5000

What is the y-intercept of the attendance function Q(p)?

• 50,500

• 23,000

• 56,000

• 28,000

How is the revenue function R(p) expressed in terms of p?

• R(p) = -5000p^2 + 50,500p

• R(p) = 5000p^2 + 50,500p

• R(p) = -2500p^2 + 50,500p

• R(p) = 2500p^2 + 50,500p

What is the first derivative of the revenue function R(p)?

• -5000p + 50,500

• 2500p + 50,500

• 5000p + 50,500

• -2500p + 50,500

At what ticket price does the revenue function reach its maximum?

• $9.00

• $10.10

• $11.00

• $12.00

What does the second derivative test confirm about the revenue function?

• It is concave up

• It is concave down

• It has no concavity

• It is linear

What is the maximum revenue achieved at the optimal ticket price?

• $500,000

• $255,255,255

• $750,000

• $1,000,000

Why is the revenue function concave down?

• Because it is a linear function

• Because it has no maximum

• Because the leading coefficient is negative

• Because the leading coefficient is positive